Using Cramer's Rule to find needed equations

[Final9mare]

Homework Statement

I am finding the minimum coefficient μ between tires and road so that cars do not slide off. I have my equations for ƩF_y and ƩF_x and I know μ = [f_s]/[/N]

So I would need to use cramer's rule on my equations to find f_s and N.

But I am not sure how to use cramer's rule for my equations.

Homework Equations

ƩF_x = Nsinθ -f_scosθ = mv²/r
ƩF_y = Ncosθ + f_ssinθ = mg

The Attempt at a Solution

I actually already have the answer but I am not sure how to use cramer's to get to it.

f_s = m(gsinθ-v²/r*cosθ)

N = m(v²/r*sinθ+gcosθ)

 

[haruspex]

At a guess (which I should not be needing to do!) the car is negotiating a bend radius r, banked at angle theta (in the helpful direction).

ƩF_x = Nsinθ -f_scosθ = mv²/r
ƩF_y = Ncosθ + f_ssinθ = mg

Sure about the sign of f_s in those? Or is this calculating the minimum speed?

I actually already have the answer but I am not sure how to use cramer's to get to it.
f_s = m(gsinθ-v²/r*cosθ)
N = m(v²/r*sinθ+gcosθ)

You have two equations and two unknowns. You're accustomed to dealing with pairs of simultaneous equations, I trust.